The Experts below are selected from a list of 97947 Experts worldwide ranked by ideXlab platform
Ralf Metzler - One of the best experts on this subject based on the ideXlab platform.
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anomalous diffusion and Ergodicity breaking in heterogeneous diffusion processes
New Journal of Physics, 2013Co-Authors: Andrey G Cherstvy, Aleksei V Chechkin, Ralf MetzlerAbstract:We demonstrate the non-Ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) ' |x| , this process yields anomalous diffusion of the form hx 2 (t)i ' t 2/(2 ) . Interestingly, in both the sub- and superdiffusive regimes we observe weak Ergodicity breaking: the scaling of the time-averaged mean-squared displacement 2 (1) remains linear in the lag time 1 and thus differs from the corresponding ensemble average hx 2 (t)i. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean-squared displacement 2 and its random features, i.e. the statistical distribution of 2 and the Ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non-ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.
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in vivo anomalous diffusion and weak Ergodicity breaking of lipid granules
Physical Review Letters, 2011Co-Authors: Jaehyung Jeon, Eli Barkai, Vincent Tejedor, Stas Burov, Christine Selhuberunkel, Kirstine Bergsorensen, Lene B Oddershede, Ralf MetzlerAbstract:Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak Ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of Ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.
K R Priolkar - One of the best experts on this subject based on the ideXlab platform.
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unusual strain glassy phase in fe doped ni2mn1 5in0 5
Applied Physics Letters, 2018Co-Authors: R Nevgi, K R PriolkarAbstract:Fe doped Ni2Mn1.5In0.5, particularly, Ni2Mn1.4Fe0.1In0.5, despite having an incommensurate, modulated 7M martensitic structure at room temperature exhibits frequency dependent behavior of storage modulus and loss which obeys the Vogel-Fulcher law as well as shows Ergodicity breaking between zero field cooled and field cooled strain measurements just above the transition temperature. Both frequency dependence and Ergodicity breaking are characteristics of a strain glassy phase and occur due to the presence of strain domains which are large enough to present signatures of long range martensitic order in diffraction but are non-interacting with other strain domains due to the presence of Fe impurities.Fe doped Ni2Mn1.5In0.5, particularly, Ni2Mn1.4Fe0.1In0.5, despite having an incommensurate, modulated 7M martensitic structure at room temperature exhibits frequency dependent behavior of storage modulus and loss which obeys the Vogel-Fulcher law as well as shows Ergodicity breaking between zero field cooled and field cooled strain measurements just above the transition temperature. Both frequency dependence and Ergodicity breaking are characteristics of a strain glassy phase and occur due to the presence of strain domains which are large enough to present signatures of long range martensitic order in diffraction but are non-interacting with other strain domains due to the presence of Fe impurities.
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Unusual Strain glassy phase in Fe doped Ni$_2$Mn$_{1.5}$In$_{0.5}$
arXiv: Materials Science, 2018Co-Authors: R Nevgi, K R PriolkarAbstract:Fe doped Ni$_2$Mn$_{1.5}$In$_{0.5}$, particularly, Ni$_2$Mn$_{1.4}$Fe$_{0.1}$In$_{0.5}$, despite having an incommensurate, modulated 7M martensitic structure at room temperature exhibits frequency dependent behavior of storage modulus and loss that obeys Vogel-Fulcher law as well as shows Ergodicity breaking between zero field cooled and field cooled strain measurements just above the transition temperature. Both, frequency dependence and Ergodicity breaking are characteristics of a strain glassy phase and occur due to presence of strain domains which are large enough to present signatures of long range martensitic order in diffraction but are non interacting with other strain domains due to presence of Fe impurity.
Eli Barkai - One of the best experts on this subject based on the ideXlab platform.
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No-go theorem for Ergodicity and an Einstein relation
Physical Review E - Statistical Nonlinear and Soft Matter Physics, 2013Co-Authors: D. Froemberg, Eli BarkaiAbstract:We provide a simple no-go theorem for Ergodicity and the generalized Einstein relation for anomalous diffusion processes. The theorem states that either Ergodicity in the sense of equal time and ensemble averaged mean squared displacements (MSD) is broken, and/or the generalized Einstein relation for time averaged diffusivity and mobility is invalid, which is in complete contrast to normal diffusion processes. We also give a general relation for the time averages of drift and MSD for ergodic (in the MSD sense) anomalous diffusion processes, showing that the ratio of these quantities depends on the measurement time. The Lévy walk model is used to exemplify the no-go theorem.
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in vivo anomalous diffusion and weak Ergodicity breaking of lipid granules
Physical Review Letters, 2011Co-Authors: Jaehyung Jeon, Eli Barkai, Vincent Tejedor, Stas Burov, Christine Selhuberunkel, Kirstine Bergsorensen, Lene B Oddershede, Ralf MetzlerAbstract:Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak Ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of Ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.
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Weak Ergodicity breaking with deterministic dynamics
EPL, 2006Co-Authors: Eli BarkaiAbstract:The concept of weak Ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak Ergodicity breaking describes a system whose dynamics is governed by a nonlinear map which generates subdiffusion deterministically. In the non-ergodic phase a non-trivial distribution of the fraction of occupation times is obtained. The visitation fraction remains uniform even in the non-ergodic phase. In this sense the non-Ergodicity is quantified, leading to a statistical mechanical description of the system even though it is not ergodic.
Sangtae Jeong - One of the best experts on this subject based on the ideXlab platform.
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toward the Ergodicity of p adic 1 lipschitz functions represented by the van der put series
Journal of Number Theory, 2013Co-Authors: Sangtae JeongAbstract:Abstract Yurova (2010) [17] and Anashin et al. (2011 [3] , preprint [4] ) characterize the Ergodicity of a 1-Lipschitz function on Z 2 in terms of the van der Put expansion. Motivated by their recent work, we provide the sufficient conditions for the Ergodicity of such a function defined on a more general setting Z p . In addition, we provide alternative proofs of two criteria (because of Anashin et al., 2011 [3] , preprint [4] and Yurova, 2010 [17] ) for an ergodic 1-Lipschitz function on Z 2 , represented by both the Mahler basis and the van der Put basis.
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toward the Ergodicity of p adic 1 lipschitz functions represented by the van der put series
arXiv: Number Theory, 2012Co-Authors: Sangtae JeongAbstract:Yurova \cite{Yu} and Anashin et al. \cite{AKY1, AKY2} characterize the Ergodicity of a 1-Lipschitz function on $\Z_2$ in terms of the van der Put expansion. Motivated by their recent work, we provide the sufficient conditions for the Ergodicity of such a function defined on a more general setting $\Z_p$. In addition, we provide alternative proofs of two criteria (because of \cite{AKY1, AKY2} and \cite{Yu}) for an ergodic 1-Lipschitz function on $\Z_2,$ represented by both the Mahler basis and the van der Put basis.
R Nevgi - One of the best experts on this subject based on the ideXlab platform.
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unusual strain glassy phase in fe doped ni2mn1 5in0 5
Applied Physics Letters, 2018Co-Authors: R Nevgi, K R PriolkarAbstract:Fe doped Ni2Mn1.5In0.5, particularly, Ni2Mn1.4Fe0.1In0.5, despite having an incommensurate, modulated 7M martensitic structure at room temperature exhibits frequency dependent behavior of storage modulus and loss which obeys the Vogel-Fulcher law as well as shows Ergodicity breaking between zero field cooled and field cooled strain measurements just above the transition temperature. Both frequency dependence and Ergodicity breaking are characteristics of a strain glassy phase and occur due to the presence of strain domains which are large enough to present signatures of long range martensitic order in diffraction but are non-interacting with other strain domains due to the presence of Fe impurities.Fe doped Ni2Mn1.5In0.5, particularly, Ni2Mn1.4Fe0.1In0.5, despite having an incommensurate, modulated 7M martensitic structure at room temperature exhibits frequency dependent behavior of storage modulus and loss which obeys the Vogel-Fulcher law as well as shows Ergodicity breaking between zero field cooled and field cooled strain measurements just above the transition temperature. Both frequency dependence and Ergodicity breaking are characteristics of a strain glassy phase and occur due to the presence of strain domains which are large enough to present signatures of long range martensitic order in diffraction but are non-interacting with other strain domains due to the presence of Fe impurities.
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Unusual Strain glassy phase in Fe doped Ni$_2$Mn$_{1.5}$In$_{0.5}$
arXiv: Materials Science, 2018Co-Authors: R Nevgi, K R PriolkarAbstract:Fe doped Ni$_2$Mn$_{1.5}$In$_{0.5}$, particularly, Ni$_2$Mn$_{1.4}$Fe$_{0.1}$In$_{0.5}$, despite having an incommensurate, modulated 7M martensitic structure at room temperature exhibits frequency dependent behavior of storage modulus and loss that obeys Vogel-Fulcher law as well as shows Ergodicity breaking between zero field cooled and field cooled strain measurements just above the transition temperature. Both, frequency dependence and Ergodicity breaking are characteristics of a strain glassy phase and occur due to presence of strain domains which are large enough to present signatures of long range martensitic order in diffraction but are non interacting with other strain domains due to presence of Fe impurity.
